Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
20 seconds
Step-by-step explanation:
I assume you mean [tex]h(t)=8\cos(\frac{\pi}{10}t)[/tex] for your function.
As the given function is in the form of [tex]f(t)=a\cos(bt+c)+d[/tex] (some textbooks may write this formula differently), the period is equal to [tex]\frac{2\pi}{|b|}[/tex]. Hence, the period of the given function is [tex]\frac{2\pi}{|\frac{\pi}{10}|}=\frac{2\pi}{1}*\frac{10}{\pi}=\frac{20\pi}{\pi}=20[/tex], or 20 seconds.
The period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.
What are some properties of a cosine function?
Suppose that we've got: [tex]f(x) = a\cos\left(\dfrac{2\pi x}{b}\right)[/tex]
Then, this function has:
- Amplitude (the maximum distance of the graph from the middle line) = a
- Period = b
For this case, we're given that:
[tex]h = 8\cos\left(\dfrac{\pi x}{10}\right)[/tex]
We can rewrite it as:
[tex]h = 8\cos\left(\dfrac{2\pi x}{20}\right)[/tex]
Thus, we get a = amplitude = 8 units(distance), and b = period = 20 units(time in seconds).
Thus, the period of the function that relates the sea level as the function of time is given by: Option D: 20 seconds.
Learn more about amplitude and period of a cosine function here:
https://brainly.com/question/4104379
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
